SOLUTION: A recording artist is offered two deals for her fourth CD release: .Royalty only: $1 per CD sold .Partial Royalty: $2000 plus $0.50 per CD sold a)Graph both linear relations

Algebra ->  Linear-equations -> SOLUTION: A recording artist is offered two deals for her fourth CD release: .Royalty only: $1 per CD sold .Partial Royalty: $2000 plus $0.50 per CD sold a)Graph both linear relations      Log On


   

Question 116515: A recording artist is offered two deals for her fourth CD release:
.Royalty only: $1 per CD sold
.Partial Royalty: $2000 plus $0.50 per CD sold
a)Graph both linear relations on the same grid.
b)Find the solution to the linear system and explain what it means.
c)Sales figures for the artist's first three CD's are shown.
CD Copies Sold
1 1500
2 3500
3 6000
Which deal do you think the artist should choose? Explain your reasoning.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
x is the number of CDs sold, and y is the amount of money earned.

y=x for the royalty only deal.
y=x%2F2%2B2000 for the partial royalty deal.

graph%28600%2C600%2C-1000%2C5000%2C-1000%2C5000%2Cx%2Cx%2F2%2B2000%29

Substitute x for y in the second equation
x=x%2F2%2B2000
x%2F2=2000
x=4000

So the solution is (4000,4000) meaning that when 4000 CDs are sold, the money earned will be 4000 for either royalty deal. It is the break-even point after which the royalty only deal becomes better for the recording artist.

Part c: Since the artist's CD sales are trending upward and the last CD sold more than the 4000 CD break even point for the deals currently offered, s/he should choose the royalty only deal.